Telex makes the best wireless mics EVER. Really. But they're about $750 each. Boo that.
I've worked with both corded mics and wireless and I have to say I *HATED* every performance in which I was attatched to something. You just don't have the freedom to manipulate your puppets as you should. In many cases, wired mics are shared. Yes they're cheaper, and that's a bonus, but what does it cost your performance?
As we learned at our show during Puppet Rampage, make sure your wires to the amp are good. If you're getting a used system, please test everything. The last thing you want is to do your sound check right before the show and then have a wire get bumped so that you have no sound, extra loud sound, or crackling coming through.
Also, when using wireless mics, always bring 4 backup batteries.
I was looking at a catalogue just the other day that came to our theater...I saw in it a portable set with speakers, mixer and all the goodies for about $250 and it all folded up into an easy-to-carry box. Great AZ Puppets' director was encouraging me to get something like that. I'll try to go in sometime this week to see to what shop it was. I know they sell online.